Throughout, let \((X,\mathfrak{M},\mu)\) be a measure space where \(\mu\) is positive.The questionIf \(f\) is of \(L^p(\mu)\), which means \(\lVert f \rVert_p=\left(\int_X |f|^p d\mu\right)^{1/p}0\), there exists some \(\delta>0\) such that \(d_2(f(x_0),f(x)) 0\) and hence \(f(x)\) is nonincreasing ……